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Numerical Stability of Lanczos Methods [PDF]
Nuclear Physics B - Proceedings Supplements, 1999 The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature.
Alan Irving +8 more
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A Lanczos Method for Approximating Composite Functions [PDF]
Applied Mathematics and Computation, 2012 We seek to approximate a composite function h(x) = g(f(x)) with a global polynomial. The standard approach chooses points x in the domain of f and computes h(x) at each point, which requires an evaluation of f and an evaluation of g. We present a Lanczos-
Eric T. Phipps +23 more
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Exact and efficient Lanczos method on a quantum computer [PDF]
Quantum, 2023 We present an algorithm that uses block encoding on a quantum computer to exactly construct a Krylov space, which can be used as the basis for the Lanczos method to estimate extremal eigenvalues of Hamiltonians.
William Kirby +2 more
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Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices
Mathematics, 2021 The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude.
Anna Concas +3 more
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The improvement of sparsity gravity inversion using an adaptive lanczos bidiagonalization method
Frontiers in Earth Science, 2023 Inversion of gravity data is one the important steps in the interpretation of practical data. The detection of sharp boundaries between anomalous bodies and host rocks is an interesting point in the geological frameworks.
Meng Zhaohai +7 more
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IEEE Access, 2023 In this paper, the symmetric Lanczos algorithm and mixed finite element method are combined to improve the efficiency and accuracy of S-parameter simulation in a broad frequency band.
Ke Chen +4 more
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Condition number estimation of preconditioned matrices. [PDF]
PLoS ONE, 2015 The present paper introduces a condition number estimation method for preconditioned matrices. The newly developed method provides reasonable results, while the conventional method which is based on the Lanczos connection gives meaningless results.
Noriyuki Kushida
doaj +1 more source
Advanced Engineering Research, 2023 Introduction. The widespread use of piezoelectric materials in various industries stimulates the study of their physical characteristics and determines the urgency of such research.
P. A. Oganesyan, O. O. Shtein
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Operator growth and Krylov complexity in Bose-Hubbard model
Journal of High Energy Physics, 2023 We study Krylov complexity of a one-dimensional Bosonic system, the celebrated Bose-Hubbard Model. The Bose-Hubbard Hamiltonian consists of interacting bosons on a lattice, describing ultra-cold atoms.
Arpan Bhattacharyya +2 more
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Orthogonal polynomials and the Lanczos method [PDF]
Banach Center Publications, 1994 Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir , Orthomin,
Brezinski C. +2 more
openaire +2 more sources